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Distributing and Combining Like Terms




This is a collection of worksheets on various topics. Click on the link and you can download the word document or the pdf version. There are short derscriptions below each QRG.

Quick Reference Guide – Distributing and Combining Like Terms

Distributive Property
  • When distributing with a positive number, multiply the number outside the parenthesis with each number inside the parenthesis.
    • Remember, the variable stays with the number, you cannot drop it.
      • 3(2x + 6) = 3(2x) + 3(6) = 6x + 18
        • This is the finished product, it cannot be simplified further
        • Don’t do this: 6x + 18 ≠ 24x or 24. They are not like terms and cannot be combined
    • Notice that the signs inside the parenthesis stay the same
      • It started with a positive plus a positive inside the parenthesis and it ends with a positive plus a positive
  • When distributing with a negative number, multiply the number outside the parenthesis with each number inside the parenthesis.
    • Remember, the variable stays with the number, you cannot drop it.
      • -5(3x – 1) = (-5)(3x) – (-5)(1) = -15x + 5
        • This is the finished product, it cannot be simplified further
        • Don’t do this: -15x + 5 ≠ -10x or -10. They are not like terms and cannot be combined
    • Notice that if you follow the proper multiplication and addition rules, the signs will all flip once. If you are unable to make this flip work, then just change the signs on your own.
      • It started with a positive minus a positive inside the parenthesis and ends with a negative plus a positive

Combining Like Terms
  • First, like terms, coefficients and constant terms need to be identified. Like terms have the same variable and constants are also like terms with no variables
    • 2x + x + 10y – 6y + 7 – 2
      • Like terms: 2x, x Coefficients: 2, 1
Like terms: 10y, -6y Coefficients: 10, -6
Constants: 7, -2
      • Notice that the signs stick with the terms and the coefficients
  • Next, like terms need to be combined. Add or subtract the coefficient and keep the variable the same
    • 2x + x = 3x
10y – 6y = 4y
7 – 2 = 5
    • 2x + x + 10y – 7y + 8 – 2 = 3x + 4y + 5
    • Remember, different variables cannot be combined, they need to be kept separate, so this cannot be simplified any further







Number Operations